OK. I see a lot of disinformation in this thread.
The note 3 doesn't support "quick charge".
The note 3 charger is a 2A charger.
USB 3.0 cables have no effect on charging, as the extra wires are just data wires.
Cheap cables do make a slight difference compared to quality cables.
Here is how chargers work (ELI5 version): a special signal is sent on the data pins from the charger that tells the device how much power it can draw.
If no signal is there, the device thinks its on a computer or cheap charger and is limited to 0.5A.
1A chargers are ubiquitous and send the 1A signal.
Most 3rd party chargers send the 1A signal even if the hardware supports more. That's how you get a 2A 2-port (1A on each port) charger, etc.
You can verify how much power is used with this: PortaPow USB Power Monitor https://www.amazon.com/dp/B00NTU18KY/
That USB power monitor is a godsend when evaluating chargers (it does not touch the data pins or affect the signal from the charger).
Interesting note: the official Samsung charger with my note 3 usually outputs about 1.7A.
I just ordered this from Amazon to help answer the question http://www.amazon.com/dp/B00NTU18KY/ref=cm_sw_r_awd_fMSSub0TY1NS3. Supposed to be pretty accurate, passively measuring current draw by placing between the charger and device.
Edit: removed shortened URL.